Planckian Birth of a Quantum de Sitter Universe

We show that the quantum universe emerging from a nonperturbative, Lorentzian sum over geometries can be described with a high accuracy by a four-dimensional de Sitter spacetime. By a scaling analysis involving Newton’s constant, we establish that the linear size of the quantum universes under study is in between 17 and 28 Planck lengths. Somewhat surprisingly, the measured quantum fluctuations around the de Sitter universe in this regime are to good approximation still describable semiclassically. The numerical evidence presented comes from a regularization of quantum gravity in terms of causal dynamical triangulations.

Figure 1

Background geometry $⟨N_3(i)⟩$: MC measurements (for fixed $N_4=362.000$) and best fit (1) yield indistinguishable curves at given plot resolution. The bars indicate the average size of quantum fluctuations.

Figure 2

Analyzing the quantum fluctuations of Fig. 1: diagonal entries $F(t,t{)}^{1/2}$ of the scaling function $F$ from (9), for $N_4=45.500$, 91.000, 181.000, and 362.000.

Figure 3

Comparing the highest eigenvector of $C(t,t^{\prime })$ and the lowest eigenvector of $M^{-1}(t,t^{\prime })$.